In 2005, Lee invested $2000 in a fund that pays 5% interest for the first 10 years, and 8% interest for every year thereafter. What will be the value of her investment in the year 2020?
2020 is 10 years at 5% and 5 years at 8%, so
2000 * 1.05^10 * 1.08^5 = 4786.76
To calculate the value of Lee's investment in the year 2020, we need to consider two periods: the first 10 years and the subsequent years.
For the first 10 years, the interest rate is 5%. We can calculate the compound interest using the formula:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount (initial investment)
r = the annual interest rate (in decimal form)
n = the number of times that interest is compounded per year
t = the number of years
In this case, Lee's initial investment is $2000, the interest rate is 5% (or 0.05 in decimal form), and the time period is 10 years.
Plugging in these values, we have:
A1 = 2000(1 + 0.05/1)^(1*10)
= 2000(1.05)^10
≈ $3257.18
So, after 10 years, the value of Lee's investment will be approximately $3257.18.
Now, for the subsequent years after the initial 10-year period, the interest rate changes to 8%. We can calculate the compound interest again using the same formula, but adjusting the interest rate and the time period.
Considering the time period from the 11th year (2016) to the 15th year (2020), which is a total of 5 years:
A2 = 3257.18(1 + 0.08/1)^(1*5)
= 3257.18(1.08)^5
≈ $4649.62
After the 15th year (2020), the value of Lee's investment will be approximately $4649.62.
Therefore, the value of Lee's investment in the year 2020 will be approximately $4649.62.